The point (2,8) is on the graph of f(x)=x3. what is the value of b if the point (0.5,8) is on the graph of f(bx)? if the point (1,3) is on the graph of y=f(x), then what is the corresponding point on the graph of y=−2f(x)?

1) Given

Since (0.5,8) lies on f(bx) ,

    Divide with on both sides

                                                           = 64

Hence b=4.

2) Given (1,3) lies on y=f(x) plugin x=1 and y=3

that is f(1) = 3

We can find corresponding point for that in y=-2f(x) by plugging in x=1.

That is y= -2f(1) = -2*3 = -6

Hence point is (1,-6)

graphs that are inverses of each other are graphs where their slopes are reciprocals of each other for example say you have an original equation of y=2x. the inverse of that graph would be y=-1/2(x). also when you see a graph where the original and the inverse is graphed the angle around intersection is 90 degrees.